Homework Help:
Comparison of width of a wavefunction in real space and momentum space

1. The problem statement, all variables and given/known data
I have solved the schrödinger equation in the momentum space for a delta potential and also transfered it into real space. So now I have to find the correlation between the width of the wavefunction in both spaces (and then motivate it physically) and I am stuck here because I don't even know where to start.

Just looking at the functions, you can approximate the characteristic width of the wave functions in position space by using [itex]\kappa x \approx 1[/itex] and in momentum space by using [itex]p / \hbar \kappa \approx 1[/itex].